# Lufthansa: to Hedge or Not to Hedge

If the DM/US\$ exchange rate were 2. 4DM/US\$ in January 1986, what would be the all in cost of the aircraft purchase under each alternative? What would be the all in cost of the aircraft purchase under each alternative if the exchange rate were 3. 4DM/US\$? Consider both fully hedging the cost and hedging exactly one half of the cost (why may you only want to hedge part of the purchase price? ). 1. Do nothing and wait and see what the exchange rate is like in January 1986. 500,000,000 USD x 2. 4DM/USD = 1,200,000,000 DM
The cost of the aircraft purchase will be 1200 million DM. 2. Cover the purchase price using forward contracts. If the company use forward contracts they have the obligation to perform, i. e. they have to buy the amount they have agreed upon in one year for the forward rate of 3. 20 DM/USD. If they fully hedging the cost the all in cost of the aircraft purchase will be: 500,000,000 USD x 3. 2DM/USD = 1,600,000,000 DM The cost of the aircraft purchase will be 1600 million DM. If they choose to hedging exactly one half of the cost the all in cost of the aircraft purchase will be: (250,000,000 USD x 2. DM/USD) + (250,000,000 USD x 3. 2DM/USD) = 1,400,000,000 DM The cost of the aircraft purchase will be 1400 million DM. 3. Cover the cost using foreign currency put options A put option gives Lufthansa the right to sell the DM at 3. 20 DM/USD in one year. Even if they don’t exercise the option they have to pay the 6 % premium. The DM has appreciated in relation to the USD and the put option is therefore out-of-the money and Lufthansa will not use the option. But they will have to pay for the premium. If they fully hedging the cost the all in cost of the aircraft purchase will be: 500,000,000 x 3. DM/USD x 0. 06 = 96,000,000 DM 500,000,000 USD x 2. 4DM/USD + 96,000,000 DM = 1,496,000,000 DM The cost of the aircraft purchase will be 1496 million DM. If they choose to hedging exactly one half of the cost the all in cost of the aircraft purchase will be: 250,000,000 x 3. 2DM/USD x 0. 06 = 48,000,000 DM 500,000,000 USD x 2. 4DM/USD + 48,000,000 DM =1,448,000,000 DM The cost of the aircraft purchase will be 1448 million DM 4. Borrow DM to buy USD dollars today and invest them for one year In this strategy Lufthansa lock in the price at today’s spot exchange rate.
They could repay the loan using the funds to be available for the purchase in one year. In January 1985 the spot exchange rate was 3. 17 DM/USD, the Eurocurrency U. S. dollar one year interest rate was 9. 5625 percent and the Eurocurrency one year deutschmark interest rate was 6. 3125 percent. If they fully hedging the cost the all in cost of the aircraft purchase will be: Borrow DM to buy 500 million USD today and invest them for one year. 500,000,000 USD/1. 095625 ? 456,360,525 USD 456,360,525 USD x 3. 17 = 1,446,662,864 DM Interest rate on the money in the end of the year: 1,446,662,864 DM x 1. 63125 = 1,537,983,458 DM Total all in cost of the aircraft purchase 1,537,983,458 DM. If they choose to hedging exactly one half of the cost the all in cost of the aircraft purchase will be: Borrow DM to buy 250 million USD today and invest them for one year. 250,000,000 USD/1. 095625 ? 228,180,262 USD 228,180,262 USD x 3. 17 ? 723,331,431 DM Interest rate on the money in the end of the year: 723,331,431 DM x 1. 063125 = 768,991,728 DM Cost of the aircraft purchase: 250,000,000 USD x 2. 4 DM/USD + 768,991,728 = 1,368,991,728 DM Total all in cost of the aircraft purchase 1,368,991,728 DM.

What would be the all in cost of the aircraft purchase under each alternative if the exchange rate were 3. 4DM/US\$? Consider both fully hedging the cost and hedging exactly one half of the cost (why may you only want to hedge part of the purchase price? ) 1. Do nothing and wait and see what the exchange rate is like in January 1986. 500,000,000 USD x 3. 4DM/USD = 1,700,000,000 DM The cost of the aircraft purchase will be 1700 million DM. 2. Cover the purchase price using forward contracts. If the company use forward contracts they have the obligation to perform, i. e. hey have to buy the amount they have agreed upon in one year for the forward rate of 3. 20 DM/USD. If they fully hedging the cost the all in cost of the aircraft purchase will be: 500,000,000 USD x 3. 2DM/USD = 1,600,000,000 DM The cost of the aircraft purchase will be 1600 million DM. If they choose to hedging exactly one half of the cost the all in cost of the aircraft purchase will be: (250,000,000 USD x 3. 4DM/USD) + (250,000,000 USD x 3. 2DM/USD) = 1,650,000,000 DM The cost of the aircraft purchase will be 1650 million DM. 3. Cover the cost using foreign currency put options
A put option gives Lufthansa the right to sell the DM at 3. 20 DM/USD in one year. Even if they don’t exercise the option they have to pay the 6 % premium. The DM has depreciated in relation to the USD and therefore the option is in-the-money and Lufthansa will use the option. If they fully hedging the cost the all in cost of the aircraft purchase will be: 500,000,000 USD x 3. 2 DM/USD x 1. 06 = 1696,000,000 DM The cost of the aircraft purchase will be 1696 million DM. If they choose to hedging exactly one half of the cost the all in cost of the aircraft purchase will be: (250,000,000 USD x 3. DM/USD) + (250,000,000 USD x 3. 2DM/USD x 1. 06) = 1,698,000,000 DM The cost of the aircraft purchase will be 1698 million DM. 4. Borrow DM to buy USD dollars today and invest them for one year In this strategy Lufthansa lock in the price at today’s spot exchange rate. They could repay the loan using the funds to be available for the purchase in one year. In January 1985 the spot exchange rate was 3. 17 DM/USD, the Eurocurrency U. S. dollar one year interest rate was 9. 5625 percent and the Eurocurrency one year deutschmark interest rate was 6. 3125 percent.
If they fully hedging the cost the all in cost of the aircraft purchase will be: Borrow DM to buy 500 million USD today and invest them for one year. 500,000,000 USD/1. 095625 ? 456,360,525 USD 456,360,525 USD x 3. 17 = 1,446,662,864 DM Interest rate on the money in the end of the year: 1,446,662,864 DM x 1. 063125 = 1,537,983,458 DM Total all in cost of the aircraft purchase 1,537,983,458 DM. If they choose to hedging exactly one half of the cost the all in cost of the aircraft purchase will be: Borrow DM to buy 250 million USD today and invest them for one year. 250,000,000 USD/1. 095625 ? 228,180,262 USD 28,180,262 USD x 3. 17 ? 723,331,431 DM Interest rate on the money in the end of the year: 723,331,431 DM x 1. 063125 = 768,991,728 DM Cost of the aircraft purchase: 250,000,000 USD x 2. 4 DM/USD + 768,991,728 = 1,368,991,728 DM Total all in cost of the aircraft purchase 1,368,991,728 DM. 2. Which alternative would you choose and why? I would not choose the first alternative and leave the amount unhedged since an appreciate of the USD against DM could change the all in cost rapidly and hence the profit. It is important to design the hedging policy based on the belief about future circumstances.
If Lufthansa really believes that the exchange rate will move in a profitable they could profit by leaving the amount unhedged. But it can be hard to predict future exchange rates and that is why a lot of companies choose to drive safe by ensuring their future financial situation through hedging. If Lufthansa would hedge all its currency risk they also take a risk and that is why I would choose to hedge only a part of the currency risk. Another aspect is that creditors’ might not like that Lufthansa is unhedged and they might also receive better interest rates if they are hedged. But of this we do not know.
Lufthansa can’t borrow any more money so we can start with excluding the forth option, i. e. the money market hedge. The put option provides the lowest all in cost if exercised but at the same it also provides the highest cost when not exercised. I know from a lecture that options were commonly used by airlines foremost to hedge against fuel prices but that they have become quiet expansive so that, at least Southwest Airlines, now days use collars instead. The money market hedge works exactly like a forward hedge and I think we have narrowed the alternatives down to the forward hedge.

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